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Anthony,
As stated in most engineering texts the standard deviation
calculation is a measure of reliability with respect to the mean ...
So by using your calculation for CV this brings the two number series
into sync based on the fact that they have different means.
This is why I personally like to do StdDev calcs based on the %
Change of the individual series. This keeps them in their proper
perspective to begin with, but the comparative results come out the
same in the end.
--- In amibroker@xxxxxxxxxxxxxxx, "Anthony Faragasso" <ajf1111@xxxx>
wrote:
>
>
> The Coefficient of Variation
>
>
>
> People who study the stock market use several different methods to
assess
> any given stock's "volatility." One of these, the standard
deviation!
> If we were to record the closing price of a stock over several
trading days,
> we could compute the standard deviation of those numbers. The SD
would be
> equal to 0 if the stock's price never changed, it would be equal to
a small
> number if the stock fluctuated just a little, and it would be equal
to a
> large number of the stock's price jumped around wildly over the
days we've
> studied.
> As proof that the SD is sometimes used as a measure of stock
volatility,
> consider these 2 statements pulled off some financially-oriented
websites:
> "Volatility: This describes the fluctuations in the price of a
stock or
> other type of security. If the price of a stock is capable of large
swings,
> the stock has a high volatility."
> "Volatility may be gauged by several measures, one of which involves
> calculating a security's standard deviation."
> Now, it seems to me the coefficient of variation does a better job
of
> assessing volatility than does the standard deviation. (As you may
recall,
> the coefficient of variation is equal to the SD ( of a variable )
divided by
> the mean.
> Let's say there are two investors (A and B) who each have $1,000 to
invest.
> Assume that Investor A buys 100 shares of a stock that's selling
for $10 a
> share, while Investor B buys 20 shares of a different stock that's
selling
> for $50 a share.
> Over 5 days, suppose the price of A's stock moves like this:
Day1=$10,
> Day2=$9, Day3=$13, Day4=$7, Day5=$11. Over this same period, suppose
> investor B's stock has this kind of fluctuation: Day1=$50, Day2=$49,
> Day3=$53, Day4=$47, Day5=$51.
> As I hope you noticed, the two stocks under consideration
fluctuated the
> same absolute amount. In each case, the SD of the 5 prices is equal
to 2.
> However, this measure of volatility misrepresents the
investors' "ups and
> downs" over the 5-day period we're considering. Investor A's
holdings
> fluctuated from $700 to $1,300 while Investor B's nestegg
fluctuated between
> $940 and $1,060.
> If we calculate the coefficient of variation (CV) instead of the
SD, look
> what happens. For investor A, the CV = 2/10 = .20; for Investor B,
the CV =
> 2/50 = .04. Comparing these CV indices, we see that Investor A's
stock is 5
> times as volatile as Investor B's stock. And doesn't that conform
to the
> fact that the overall value of Investor A's stock (with a range
from $1,300
> to $700) changes far more than does the total value of Investor B's
stock
> (where the range extends only from $1,060 to $940).
> I hope this little example shows how the coefficient of variation
can be useful when trying to assess the degree of "spread" within a
set of numbers. As illustrated by the performance of the two
hypothetical stocks, the SD disregards the level of the mean when it
assess variability. The SD computes how variable the scores are
around the mean, but the size of the mean is not taken into
consideration. In contrast, the coefficient of variation looks at the
spread of scores (around the mean), adjusted for the size of the mean.
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